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   <div id="projectbrief">A library for carrying out Multivariate Kernel Smoothing--designed to be fast and flexible for large data processing.</div>
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<div class="title">matrix_inverse.h</div>  </div>
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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">// header file for matrix template class</span>
<a name="l00002"></a>00002 <span class="comment">// NOTE:  all matrices handled here must be SQUARE </span>
<a name="l00003"></a>00003 <span class="comment">//        (i.e., # rows = # columns)</span>
<a name="l00004"></a>00004 <span class="comment">// in addition, all DIAGONAL ELEMENTS MUST BE NONZERO</span>
<a name="l00005"></a>00005 <span class="comment">// written by Mike Dinolfo 12/98</span>
<a name="l00006"></a>00006 <span class="comment">// version 1.0</span>
<a name="l00007"></a>00007 
<a name="l00008"></a>00008 <span class="preprocessor">#ifndef __mjdmatrix_h</span>
<a name="l00009"></a>00009 <span class="preprocessor"></span><span class="preprocessor">#define __mjdmatrix_h</span>
<a name="l00010"></a>00010 <span class="preprocessor"></span><span class="preprocessor">#include &lt;iostream&gt;</span>
<a name="l00011"></a>00011 <span class="comment">// generic object (class) definition of matrix:</span>
<a name="l00012"></a>00012 <span class="keyword">template</span> &lt;<span class="keyword">class</span> D&gt; <span class="keyword">class </span>MatrixClass{
<a name="l00013"></a>00013   <span class="comment">// NOTE: maxsize determines available memory storage, but</span>
<a name="l00014"></a>00014   <span class="comment">// actualsize determines the actual size of the stored matrix in use</span>
<a name="l00015"></a>00015   <span class="comment">// at a particular time.</span>
<a name="l00016"></a>00016   <span class="keywordtype">int</span> maxsize;  <span class="comment">// max number of rows (same as max number of columns)</span>
<a name="l00017"></a>00017   <span class="keywordtype">int</span> actualsize;  <span class="comment">// actual size (rows, or columns) of the stored matrix</span>
<a name="l00018"></a>00018   D* data;      <span class="comment">// where the data contents of the matrix are stored</span>
<a name="l00019"></a>00019   <span class="keywordtype">void</span> allocate()   {
<a name="l00020"></a>00020     <span class="keyword">delete</span>[] data;
<a name="l00021"></a>00021     data = <span class="keyword">new</span> D [maxsize*maxsize];
<a name="l00022"></a>00022     };
<a name="l00023"></a>00023   MatrixClass() {};                  <span class="comment">// private ctor&#39;s</span>
<a name="l00024"></a>00024   MatrixClass(<span class="keywordtype">int</span> newmaxsize) {MatrixClass(newmaxsize,newmaxsize);};
<a name="l00025"></a>00025 <span class="keyword">public</span>:
<a name="l00026"></a>00026   MatrixClass(<span class="keywordtype">int</span> newmaxsize, <span class="keywordtype">int</span> newactualsize)  { <span class="comment">// the only public ctor</span>
<a name="l00027"></a>00027     <span class="keywordflow">if</span> (newmaxsize &lt;= 0) newmaxsize = 5;
<a name="l00028"></a>00028     maxsize = newmaxsize; 
<a name="l00029"></a>00029     <span class="keywordflow">if</span> ((newactualsize &lt;= newmaxsize)&amp;&amp;(newactualsize&gt;0))
<a name="l00030"></a>00030       actualsize = newactualsize;
<a name="l00031"></a>00031     <span class="keywordflow">else</span> 
<a name="l00032"></a>00032       actualsize = newmaxsize;
<a name="l00033"></a>00033     <span class="comment">// since allocate() will first call delete[] on data:</span>
<a name="l00034"></a>00034     data = 0;
<a name="l00035"></a>00035     allocate();
<a name="l00036"></a>00036     };
<a name="l00037"></a>00037   ~MatrixClass() { <span class="keyword">delete</span>[] data; };
<a name="l00038"></a>00038   <span class="keywordtype">void</span> comparetoidentity()  {
<a name="l00039"></a>00039     <span class="keywordtype">int</span> worstdiagonal = 0;
<a name="l00040"></a>00040     D maxunitydeviation = 0.0;
<a name="l00041"></a>00041     D currentunitydeviation;
<a name="l00042"></a>00042     <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> i = 0; i &lt; actualsize; i++ )  {
<a name="l00043"></a>00043       currentunitydeviation = data[i*maxsize+i] - 1.;
<a name="l00044"></a>00044       <span class="keywordflow">if</span> ( currentunitydeviation &lt; 0.0) currentunitydeviation *= -1.;
<a name="l00045"></a>00045       <span class="keywordflow">if</span> ( currentunitydeviation &gt; maxunitydeviation )  {
<a name="l00046"></a>00046            maxunitydeviation = currentunitydeviation;
<a name="l00047"></a>00047            worstdiagonal = i;
<a name="l00048"></a>00048            }
<a name="l00049"></a>00049       }
<a name="l00050"></a>00050     <span class="keywordtype">int</span> worstoffdiagonalrow = 0;
<a name="l00051"></a>00051     <span class="keywordtype">int</span> worstoffdiagonalcolumn = 0;
<a name="l00052"></a>00052     D maxzerodeviation = 0.0;
<a name="l00053"></a>00053     D currentzerodeviation ;
<a name="l00054"></a>00054     <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> i = 0; i &lt; actualsize; i++ )  {
<a name="l00055"></a>00055       <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> j = 0; j &lt; actualsize; j++ )  {
<a name="l00056"></a>00056         <span class="keywordflow">if</span> ( i == j ) <span class="keywordflow">continue</span>;  <span class="comment">// we look only at non-diagonal terms</span>
<a name="l00057"></a>00057         currentzerodeviation = data[i*maxsize+j];
<a name="l00058"></a>00058         <span class="keywordflow">if</span> ( currentzerodeviation &lt; 0.0) currentzerodeviation *= -1.0;
<a name="l00059"></a>00059         <span class="keywordflow">if</span> ( currentzerodeviation &gt; maxzerodeviation )  {
<a name="l00060"></a>00060           maxzerodeviation = currentzerodeviation;
<a name="l00061"></a>00061           worstoffdiagonalrow = i;
<a name="l00062"></a>00062           worstoffdiagonalcolumn = j;
<a name="l00063"></a>00063           }
<a name="l00064"></a>00064 
<a name="l00065"></a>00065         }
<a name="l00066"></a>00066       }
<a name="l00067"></a>00067     cout &lt;&lt; <span class="stringliteral">&quot;Worst diagonal value deviation from unity: &quot;</span> 
<a name="l00068"></a>00068        &lt;&lt; maxunitydeviation &lt;&lt; <span class="stringliteral">&quot; at row/column &quot;</span> &lt;&lt; worstdiagonal &lt;&lt; endl;
<a name="l00069"></a>00069     cout &lt;&lt; <span class="stringliteral">&quot;Worst off-diagonal value deviation from zero: &quot;</span> 
<a name="l00070"></a>00070        &lt;&lt; maxzerodeviation &lt;&lt; <span class="stringliteral">&quot; at row = &quot;</span> &lt;&lt; worstoffdiagonalrow 
<a name="l00071"></a>00071        &lt;&lt; <span class="stringliteral">&quot;, column = &quot;</span> &lt;&lt; worstoffdiagonalcolumn &lt;&lt; endl;
<a name="l00072"></a>00072   }
<a name="l00073"></a>00073   <span class="keywordtype">void</span> settoproduct(MatrixClass&amp; left, MatrixClass&amp; right)  {
<a name="l00074"></a>00074     actualsize = left.getactualsize();
<a name="l00075"></a>00075     <span class="keywordflow">if</span> ( maxsize &lt; left.getactualsize() )   {
<a name="l00076"></a>00076       maxsize = left.getactualsize();
<a name="l00077"></a>00077       allocate();
<a name="l00078"></a>00078       }
<a name="l00079"></a>00079     <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> i = 0; i &lt; actualsize; i++ )
<a name="l00080"></a>00080       <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> j = 0; j &lt; actualsize; j++ )  {
<a name="l00081"></a>00081         D sum = 0.0;
<a name="l00082"></a>00082         D leftvalue, rightvalue;
<a name="l00083"></a>00083         <span class="keywordtype">bool</span> success;
<a name="l00084"></a>00084         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> c = 0; c &lt; actualsize; c++)  {
<a name="l00085"></a>00085             left.getvalue(i,c,leftvalue,success);
<a name="l00086"></a>00086             right.getvalue(c,j,rightvalue,success);
<a name="l00087"></a>00087             sum += leftvalue * rightvalue;
<a name="l00088"></a>00088             }
<a name="l00089"></a>00089         setvalue(i,j,sum);
<a name="l00090"></a>00090         }
<a name="l00091"></a>00091     }
<a name="l00092"></a>00092   <span class="keywordtype">void</span> copymatrix(MatrixClass&amp;  source)  {
<a name="l00093"></a>00093     actualsize = source.getactualsize();
<a name="l00094"></a>00094     <span class="keywordflow">if</span> ( maxsize &lt; source.getactualsize() )  {
<a name="l00095"></a>00095       maxsize = source.getactualsize();
<a name="l00096"></a>00096       allocate();
<a name="l00097"></a>00097       }
<a name="l00098"></a>00098     <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> i = 0; i &lt; actualsize; i++ )
<a name="l00099"></a>00099       <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> j = 0; j &lt; actualsize; j++ )  {
<a name="l00100"></a>00100         D value;
<a name="l00101"></a>00101         <span class="keywordtype">bool</span> success;
<a name="l00102"></a>00102         source.getvalue(i,j,value,success);
<a name="l00103"></a>00103         data[i*maxsize+j] = value;
<a name="l00104"></a>00104         }
<a name="l00105"></a>00105     };
<a name="l00106"></a>00106   <span class="keywordtype">void</span> setactualsize(<span class="keywordtype">int</span> newactualsize) {
<a name="l00107"></a>00107     <span class="keywordflow">if</span> ( newactualsize &gt; maxsize )
<a name="l00108"></a>00108       {
<a name="l00109"></a>00109         maxsize = newactualsize ; <span class="comment">// * 2;  // wastes memory but saves</span>
<a name="l00110"></a>00110                                       <span class="comment">// time otherwise required for</span>
<a name="l00111"></a>00111                                       <span class="comment">// operation new[]</span>
<a name="l00112"></a>00112         allocate();
<a name="l00113"></a>00113       }
<a name="l00114"></a>00114     <span class="keywordflow">if</span> (newactualsize &gt;= 0) actualsize = newactualsize;
<a name="l00115"></a>00115     };
<a name="l00116"></a>00116   <span class="keywordtype">int</span> getactualsize() { <span class="keywordflow">return</span> actualsize; };
<a name="l00117"></a>00117   <span class="keywordtype">void</span> getvalue(<span class="keywordtype">int</span> row, <span class="keywordtype">int</span> column, D&amp; returnvalue, <span class="keywordtype">bool</span>&amp; success)   {
<a name="l00118"></a>00118     <span class="keywordflow">if</span> ( (row&gt;=maxsize) || (column&gt;=maxsize) 
<a name="l00119"></a>00119       || (row&lt;0) || (column&lt;0) )
<a name="l00120"></a>00120       {  success = <span class="keyword">false</span>;
<a name="l00121"></a>00121          <span class="keywordflow">return</span>;    }
<a name="l00122"></a>00122     returnvalue = data[ row * maxsize + column ];
<a name="l00123"></a>00123     success = <span class="keyword">true</span>;
<a name="l00124"></a>00124     };
<a name="l00125"></a>00125   <span class="keywordtype">bool</span> setvalue(<span class="keywordtype">int</span> row, <span class="keywordtype">int</span> column, D newvalue)  {
<a name="l00126"></a>00126     <span class="keywordflow">if</span> ( (row &gt;= maxsize) || (column &gt;= maxsize) 
<a name="l00127"></a>00127         || (row&lt;0) || (column&lt;0) ) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00128"></a>00128     data[ row * maxsize + column ] = newvalue;
<a name="l00129"></a>00129     <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00130"></a>00130     };
<a name="l00131"></a>00131   <span class="keywordtype">float</span> invert()  {
<a name="l00132"></a>00132 
<a name="l00133"></a>00133     <span class="comment">/*</span>
<a name="l00134"></a>00134 <span class="comment">    cout&lt;&lt;&quot;Outputting matrix to be inverted: &quot;&lt;&lt;endl;</span>
<a name="l00135"></a>00135 <span class="comment">    for(int i=0; i&lt;maxsize; i++)</span>
<a name="l00136"></a>00136 <span class="comment">      {</span>
<a name="l00137"></a>00137 <span class="comment">        for(int j=0; j&lt;maxsize; j++)</span>
<a name="l00138"></a>00138 <span class="comment">          {</span>
<a name="l00139"></a>00139 <span class="comment">            cout&lt;&lt;data[i*maxsize+j]&lt;&lt;&quot; &quot;;</span>
<a name="l00140"></a>00140 <span class="comment">            </span>
<a name="l00141"></a>00141 <span class="comment">          }</span>
<a name="l00142"></a>00142 <span class="comment">        cout&lt;&lt;endl;</span>
<a name="l00143"></a>00143 <span class="comment">      }</span>
<a name="l00144"></a>00144 <span class="comment">    */</span>  
<a name="l00145"></a>00145 
<a name="l00146"></a>00146     <span class="keywordflow">if</span> (actualsize &lt;= 0) <span class="keywordflow">return</span> 0;  <span class="comment">// sanity check</span>
<a name="l00147"></a>00147     <span class="keywordflow">if</span> (actualsize == 1) 
<a name="l00148"></a>00148       {
<a name="l00149"></a>00149         <span class="keywordtype">float</span> determinant=data[0];
<a name="l00150"></a>00150         data[0]=1.0/data[0];
<a name="l00151"></a>00151         <span class="keywordflow">return</span> determinant; 
<a name="l00152"></a>00152       } 
<a name="l00153"></a>00153     <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=1; i &lt; actualsize; i++) data[i] /= data[0]; <span class="comment">// normalize row 0</span>
<a name="l00154"></a>00154     <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=1; i &lt; actualsize; i++)  { 
<a name="l00155"></a>00155       <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j=i; j &lt; actualsize; j++)  { <span class="comment">// do a column of L</span>
<a name="l00156"></a>00156         D sum = 0.0;
<a name="l00157"></a>00157         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; i; k++) 
<a name="l00158"></a>00158             sum += data[j*maxsize+k] * data[k*maxsize+i];
<a name="l00159"></a>00159         data[j*maxsize+i] -= sum;
<a name="l00160"></a>00160         }
<a name="l00161"></a>00161       <span class="keywordflow">if</span> (i == actualsize-1) <span class="keywordflow">continue</span>;
<a name="l00162"></a>00162       <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j=i+1; j &lt; actualsize; j++)  {  <span class="comment">// do a row of U</span>
<a name="l00163"></a>00163         D sum = 0.0;
<a name="l00164"></a>00164         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; i; k++)
<a name="l00165"></a>00165             sum += data[i*maxsize+k]*data[k*maxsize+j];
<a name="l00166"></a>00166         data[i*maxsize+j] = 
<a name="l00167"></a>00167            (data[i*maxsize+j]-sum) / data[i*maxsize+i];
<a name="l00168"></a>00168         }
<a name="l00169"></a>00169       }
<a name="l00170"></a>00170 
<a name="l00171"></a>00171     <span class="comment">//intercept to get determinant</span>
<a name="l00172"></a>00172     <span class="keywordtype">float</span> det=1;
<a name="l00173"></a>00173     
<a name="l00174"></a>00174     <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0; i&lt;maxsize; i++)
<a name="l00175"></a>00175       det*=data[i*maxsize+i];
<a name="l00176"></a>00176 
<a name="l00177"></a>00177     <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> i = 0; i &lt; actualsize; i++ )  <span class="comment">// invert L</span>
<a name="l00178"></a>00178       <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> j = i; j &lt; actualsize; j++ )  {
<a name="l00179"></a>00179         D x = 1.0;
<a name="l00180"></a>00180         <span class="keywordflow">if</span> ( i != j ) {
<a name="l00181"></a>00181           x = 0.0;
<a name="l00182"></a>00182           <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> k = i; k &lt; j; k++ ) 
<a name="l00183"></a>00183               x -= data[j*maxsize+k]*data[k*maxsize+i];
<a name="l00184"></a>00184           }
<a name="l00185"></a>00185         data[j*maxsize+i] = x / data[j*maxsize+j];
<a name="l00186"></a>00186         }
<a name="l00187"></a>00187     <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> i = 0; i &lt; actualsize; i++ )   <span class="comment">// invert U</span>
<a name="l00188"></a>00188       <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> j = i; j &lt; actualsize; j++ )  {
<a name="l00189"></a>00189         <span class="keywordflow">if</span> ( i == j ) <span class="keywordflow">continue</span>;
<a name="l00190"></a>00190         D sum = 0.0;
<a name="l00191"></a>00191         <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> k = i; k &lt; j; k++ )
<a name="l00192"></a>00192             sum += data[k*maxsize+j]*( (i==k) ? 1.0 : data[i*maxsize+k] );
<a name="l00193"></a>00193         data[i*maxsize+j] = -sum;
<a name="l00194"></a>00194         }
<a name="l00195"></a>00195     <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> i = 0; i &lt; actualsize; i++ )   <span class="comment">// final inversion</span>
<a name="l00196"></a>00196       <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> j = 0; j &lt; actualsize; j++ )  {
<a name="l00197"></a>00197         D sum = 0.0;
<a name="l00198"></a>00198         <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> k = ((i&gt;j)?i:j); k &lt; actualsize; k++ )  
<a name="l00199"></a>00199             sum += ((j==k)?1.0:data[j*maxsize+k])*data[k*maxsize+i];
<a name="l00200"></a>00200         data[j*maxsize+i] = sum;
<a name="l00201"></a>00201       }
<a name="l00202"></a>00202 
<a name="l00203"></a>00203     <span class="comment">/*</span>
<a name="l00204"></a>00204 <span class="comment">    cout&lt;&lt;&quot;Outputting inverted matrix: &quot;&lt;&lt;endl;</span>
<a name="l00205"></a>00205 <span class="comment">    for(int i=0; i&lt;maxsize; i++)</span>
<a name="l00206"></a>00206 <span class="comment">      {</span>
<a name="l00207"></a>00207 <span class="comment">        for(int j=0; j&lt;maxsize; j++)</span>
<a name="l00208"></a>00208 <span class="comment">          {</span>
<a name="l00209"></a>00209 <span class="comment">            cout&lt;&lt;data[i*maxsize+j]&lt;&lt;&quot; &quot;;</span>
<a name="l00210"></a>00210 <span class="comment">            </span>
<a name="l00211"></a>00211 <span class="comment">          }</span>
<a name="l00212"></a>00212 <span class="comment">        cout&lt;&lt;endl;</span>
<a name="l00213"></a>00213 <span class="comment">      }</span>
<a name="l00214"></a>00214 <span class="comment">    */</span>
<a name="l00215"></a>00215 
<a name="l00216"></a>00216 
<a name="l00217"></a>00217     <span class="comment">//return determinant</span>
<a name="l00218"></a>00218     <span class="keywordflow">return</span> det;
<a name="l00219"></a>00219   }
<a name="l00220"></a>00220 
<a name="l00221"></a>00221 };
<a name="l00222"></a>00222 <span class="preprocessor">#endif</span>
<a name="l00223"></a>00223 <span class="preprocessor"></span>
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